The sheriff's police cruiser switches from a 1973 Plymouth Satellite Custom to a 1973 Dodge Coronet where Frady takes a shortcut through a construction site. And when he crashes the cop car in a local Safeway, the cop cruiser is a 1973 Plymouth.
The politician played by Jim Davis is called George Hammond by the investigating committee at the end, but earlier in the film when we first see his picture in a newspaper on the flight, the caption beneath his photo says John Hammond.
The score in the "Pong" game between the scientist and the monkey.
In the opening Independence Day parade sequence, there are no leaves on the tree branches visible as the senator and his wife pass by, but the leaves would be full and green on July 4th in Seattle.
Senator Hammond is killed by three shots fired at very brief intervals. The slow-firing bolt action rifle left by Parallax for police to find would hardly be plausible as Hammond's murder weapon. (Possible deliberate error by the filmmakers, as JFK's assassination with a similar bolt-action rifle was deemed "plausible" by the Warren Commission shortly before this film was made.)
The assassination suspect rolls off the white roof of the Space Needle and you hear the scream of an uninterrupted fall all the way to the ground. In reality, he would be falling onto the observation deck surrounding the restaurant.